An adaptive SVR-HDMR model for approximating high dimensional problems

Abstract

Purpose

Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. The purpose of this paper is to use support vector regression with high dimensional model representation (SVR-HDMR) model to obtain accurate metamodels for high dimensional problems with a few sampling points.

Design/methodology/approach

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. Support vector regression (SVR) method can approximate the underlying functions with a small subset of sample points. Dividing Rectangles (DIRECT) algorithm is a deterministic sampling method.

Findings

This paper proposes a new form of HDMR by integrating the SVR, termed as SVR-HDMR. And an intelligent sampling strategy, namely, DIRECT method, is adopted to improve the efficiency of SVR-HDMR.

Originality/value

Compared to other metamodeling techniques, the accuracy and efficiency of SVR-HDMR were significantly improved. The SVR-HDMR helped engineers understand the essence of underlying problems visually.

Citation

Huang, Z., Qiu, H., Zhao, M., Cai, X. and Gao, L. (2015), "An adaptive SVR-HDMR model for approximating high dimensional problems", Engineering Computations, Vol. 32 No. 3, pp. 643-667. https://doi.org/10.1108/EC-08-2013-0208